References
- Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. http://doi.org/10.12989/gae.2019.17.2.175.
- Ahmed, R.A., Mustafa, N.M., Faleh, N.M. and Fenjan, R.M. (2020), "Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method", Struct. Eng. Mech., 76(3), 413-420. https://doi.org/10.12989/sem.2020.76.3.413.
- Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963.
- Atmane, H.A., Tounsi, A and Bernard, F. (2015a), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13, 71-84. https://doi.org/10.1007/s10999-015-9318-x.
- Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015b), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. http://doi.org/10.12989/scs.2015.19.2.369.
- Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. http://doi.org/10.12989/eas.2018.14.2.103.
- Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. http://dx.doi.org/10.12989/scs.2015.18.4.1063.
- Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. http://doi.org/10.12989/sem.2017.62.6.695.
- Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803.
- Faleh, N.M., Abboud, I.K. and Nori, A.F. (2020), "Nonlinear stability of smart nonlocal magneto-electro-thermo-elastic beams with geometric imperfection and piezoelectric phase effects", Smart Struct. Syst., 25(6), 707-717. https://doi.org/10.12989/sss.2020.25.6.707.
- Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
- Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020a), "Nonlinear vibration characteristics of refined higher-order multi-phase piezo-magnetic nanobeams", Eur. Phys. J. Plus, 135(5), 439. https://doi.org/10.1140/epjp/s13360-020-00399-4.
- Fenjan, R.M., Ahmed, R.A., Faleh, N.M. and Hani, F.M. (2020e), "Static stability analysis of smart nonlocal thermo-piezo-magnetic plates via a quasi-3D formulation", Smart Struct. Syst., 26(1), 77-87. https://doi.org/10.12989/sss.2020.26.1.077.
- Fenjan, R.M., Ahmed, R.A., Hamad, L.B. and Faleh, N.M. (2020b), "A review of numerical approach for dynamic response of strain gradient metal foam shells under constant velocity moving loads", Adv. Comput. Des., 5(4), 349-362. https://doi.org/10.12989/acd.2020.5.4.349.
- Fenjan, R.M., Faleh, N.M. and Ahmed, R.A. (2020c), "Geometrical imperfection and thermal effects on nonlinear stability of microbeams made of graphene-reinforced nanocomposites", Adv. Nano Res., 9(3), 147-156. https://doi.org/10.12989/anr.2020.9.3.147.
- Fenjan, R.M., Faleh, N.M. and Ridha, A.A. (2020d), "Strain gradient based static stability analysis of composite crystalline shell structures having porosities", Steel Compos. Struct., 36(6), 631-642. https://doi.org/10.12989/scs.2020.36.6.631.
- Han, S.C., Park, W.T. and Jung, W.Y. (2015), "A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface", Compos. Struct., 131, 1081-1089. https://doi.org/10.1016/j.compstruct.2015.06.025.
- Hosseini, M. and Jamalpoor, A. (2015), "Analytical solution for thermomechanical vibration of double-viscoelastic nanoplate-systems made of functionally graded materials", J. Therm. Stress., 38(12), 1428-1456. https://doi.org/10.1080/01495739.2015.1073986.
- Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. http://doi.org/10.12989/scs.2016.22.2.257.
- Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., 65(5), 621-631. http://doi.org/10.12989/sem.2018.65.5.621.
- Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. http://doi.org/10.12989/sem.2017.64.4.391.
- Kunbar, L.A.H., Hamad, L.B., Ahmed, R.A. and Faleh, N.M. (2020), "Nonlinear vibration of smart nonlocal magneto-electro-elastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects", Smart Struct. Syst., 25(5), 619-630. https://doi.org/10.12989/sss.2020.25.5.619.
- Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A. and Bedia, E.A.A. (2018), "On the effect of the micromechanical models on the free vibration of rectangular FGM plate resting on elastic foundation", Earthq. Struct., 14(2), 117-128. https://doi.org/10.12989/eas.2018.14.2.117.
- Mechab, B., Mechab, I., Benaissa, S., Ameri, M. and Serier, B. (2016), "Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler-Pasternak elastic foundations", Appl. Math. Model., 40(2), 738-749. https://doi.org/10.1016/j.apm.2015.09.093.
- Mehala, T., Belabed, Z., Tounsi, A. and Beg, O.A. (2018), "Investigation of influence of homogenization models on stability and dynamics of FGM plates on elastic foundations", Geomech. Eng., 16(3), 257-271. http://doi.org/10.12989/gae.2018.16.3.257.
- Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031.
- Reddy, J.N. (1990), "A general non-linear third-order theory of plates with moderate thickness", Int. J. Nonlin. Mech., 25(6), 677-686. https://doi.org/10.1016/0020-7462(90)90006-U.
- Sadoun, M., Houari, M.S.A., Bakora, A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory", Geomech. Eng., 16(2), 141-150. http://doi.org/10.12989/gae.2018.16.2.141.
- Taj, M.G., Chakrabarti, A. and Sheikh, A.H. (2013), "Analysis of functionally graded plates using higher order shear deformation theory", Appl. Math. Model., 37(18), 8484-8494. https://doi.org/10.1016/j.apm.2013.03.058.
- Thai, H.T., Vo, T., Bui, T. and Nguyen, T.K. (2014), "A quasi-3D hyperbolic shear deformation theory for functionally graded plates", Acta Mechanica, 225(3), 951-964. https://doi.org/10.1007/s00707-013-0994-z.
- Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143.
- Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693.
- Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51(11), 869-880. https://doi.org/10.1016/j.ijmecsci.2009.09.026.
- Zenkour, A.M. (2016), "Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium", Physica E: Low Dimens. Syst. Nanostruct., 79, 87-97. https://doi.org/10.1016/j.physe.2015.12.003.
- Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., 64(2), 145-153. http://doi.org/10.12989/sem.2017.64.2.145.